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Conference on Lasers and Electro-Optics

Continuous-Variable Quantum Erasure Correcting Code

Mikael Lassen, Metin Sabuncu, Alexander Huck, Julien Niset, Nicolas J. Cerf, Gerd Leuchs, Ulrik L. Andersen

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We experimentally demonstrate a continuous variable quantum erasure-correcting code, which protects coherent states of light against complete erasure. The scheme encodes two coherent states into a bi-party entangled state, and the resulting 4-mode code is conveyed through 4 independent channels that randomly erases the signal. We show experimentally that the transmitted state can be corrected by performing a syndrome measurement followed by a corrective transformation.

DOI
10.1364/qels.2010.jthe25

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We experimentally demonstrate a continuous variable quantum erasure-correcting code, which protects coherent states of light against complete erasure. The scheme encodes two coherent states into a bi-party entangled state, and the resulting 4-mode code is conveyed through 4 independent channels that randomly erases the signal. We show experimentally that the transmitted state can be corrected by performing a syndrome measurement followed by a corrective transformation.
Quantum states of light being transmitted via realistic free-space channels often suffer erasure errors due to several factors such as coupling inefficiencies between transmitter and receiver. In this work, an error correction code capable of protecting a single-mode quantum state against erasures is presented. Our three-mode code protects a single-mode Continuous Variable (CV) state via a bipartite CV entangled state. In realistic deployments, it can almost completely reverse a single erasure on the encoded state, and for two erasures can it improve the fidelities of received states relative to direct transmission. The bipartite entangled state used in the encoding can be Gaussian or non-Gaussian, with the latter further enhancing the performance of the code. Our new code is the simplest code known that protects a single mode against erasures and should prove useful in the construction of practical CV quantum networks that rely on free-space optics.
We devise a scheme that protects quantum coherent states of light from probabilistic losses, thus achieving the first continuous-variable quantum erasure-correcting code. If the occurrence of erasures can be probed, then the decoder enables, in principle, a perfect recovery of the original light states. Otherwise, if supplemented with postselection based on homodyne detection, this code can be turned into an efficient erasure-filtration scheme. The experimental feasibility of the proposed protocol is carefully addressed.
Quantum error correction protects the quantum state against noise and decoherence in quantum communication and quantum computation, which enables one to perform fault-torrent quantum information processing. We experimentally demonstrate a quantum error correction scheme with a five-wave-packet code against a single stochastic error, the original theoretical model of which was firstly proposed by S. L. Braunstein and T. A. Walker. Five submodes of a continuous variable cluster entangled state of light are used for five encoding channels. Especially, in our encoding scheme the information of the input state is only distributed on three of the five channels and thus any error appearing in the remained two channels never affects the output state, i.e. the output quantum state is immune from the error in the two channels. The stochastic error on a single channel is corrected for both vacuum and squeezed input states and the achieved fidelities of the output states are beyond the corresponding classical limit.
Quantum erasure-correcting code, which corrects the erasure in the transmission of quantum information, is an important protocol in quantum information. In the continuous variable regime, the feed-forward technique is needed for realizing quantum erasure-correcting code. This feed-forward technique involves optic-electro and electro-optic conversions, limiting the bandwidth of quantum erasure-correcting code. Moreover, in the previous continuous variable quantum erasure-correcting code, only two modes are protected against erasure, limiting the applications of quantum erasure-correcting code in high-capacity quantum information processing. In this Letter, by utilizing the orbital angular momentum (OAM) multiplexed entanglement in the encoding part and replacing the feed-forward technique with OAM mode-matched phase-sensitive amplifier in the decoding part, we experimentally demonstrate a scheme of OAM multiplexed deterministic all-optical quantum erasure-correcting code. We experimentally demonstrate that four orthogonal modes can be simultaneously protected against one arbitrary erasure. Our results provide an all-optical platform to implement quantum erasure-correcting code and may have potential applications in implementing all-optical fault-tolerant quantum information processing.
We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.
Quantum capacity, as the key figure of merit for a given quantum channel, upper bounds the channel's ability in transmitting quantum information. Identifying different types of channels, evaluating the corresponding quantum capacity, and finding the capacity-approaching coding scheme are the major tasks in quantum communication theory. Quantum channel in discrete variables has been discussed enormously based on various error models, while error model in the continuous variable channel has been less studied due to the infinite dimensional problem. In this paper, we investigate a general continuous variable quantum erasure channel. By defining an effective subspace of the continuous variable system, we find a continuous variable random coding model. We then derive the quantum capacity of the continuous variable erasure channel in the framework of decoupling theory. The discussion in this paper fills the gap of a quantum erasure channel in continuous variable setting and sheds light on the understanding of other types of continuous variable quantum channels.